We formulate the AVS problem as a Partially Observable Markov Decision Process (POMDP), which is a standard framework for modeling sequential decision processes under uncertainty in dynamical environments [1]}.
A POMDP is a tuple \((S,A,O,T,Z,R,\gamma )\) , where \(S\)  is a finite set of partially observable states, \(A\)  is a finite set of actions, \(Z\)  is a finite set of observations, \(T\) : \(S\times A \rightarrow \Pi (S)\)  is the state-transition model, \(O\) : \(S\times A \rightarrow \Pi (Z)\)  is the observation model, \(R\) : \(S \times A \rightarrow \mathbb {R}\)  is the reward function and \(\gamma \in [0,1)\)  is a discount factor.
Agents operating POMDPs aim to maximise their expected total discounted reward \(E[\sum _{t=0}^{\infty } \gamma ^t R(s_t,a_t)]\) , by choosing the best action \(a_t\)  in each state \(s_t\) , where \(t\)  is the time instant; \(\gamma \)  reduces the weight of distant rewards and ensures the (infinite) sum's convergence. The partial observability of the state is dealt with by considering at each time-step a probability distribution over all the states, called the belief \(B\) .
POMDP solvers are algorithms that compute, in an exact or approximate way, a policy for POMDPs, namely a function \(\pi \) : \(B \rightarrow A\)  that maps beliefs to actions.
